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http://dx.doi.org/10.5831/HMJ.2020.42.1.151

CHARACTERIZATION OF WARPED PRODUCT SEMI-SLANT SUBMANIFOLDS OF A LOCALLY PRODUCT RIEMANNIAN MANIFOLD  

Ali, Rifaqat (Department of Mathematics, College of Sciences and Arts, Muhayil, King Khalid University)
Publication Information
Honam Mathematical Journal / v.42, no.1, 2020 , pp. 151-160 More about this Journal
Abstract
In this paper, we obtain some necessary and sufficient conditions such that a semi-slant submanifold in a locally product Riemannian manifold reduces to a warped product semi-slant submanifold and also give an example supported this characterization.
Keywords
Warped products; semi-slant; characterization; locally product Riemannian manifold;
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1 Ali, A., Laurian-Ioan, P., Alkhaldi, A. H., Alqahtani, L . S., Ricci curvature on warped product submanifolds of complex space forms and its applications. Int. J. Geom. Meth. Moder. Phy., (2019) https://doi.org/10.1142/S0219887819501421.
2 A. Ali, S. Uddin, W. A. M. Othman, Geometry of warped product pointwise semi-slant submanifolds of Kaehler manifolds, Filomat 32 (2017), 3771-3788.
3 A. Ali, P. Luarian, Geometry of warped product immersions of Kenmotsu space forms and its applications to slant immersions, J. Geom. Phy., 114, (2017); pp 276-290.   DOI
4 A. Ali, C. Ozel, Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications, Int. J. Geom. Meth. Mod. Phy., 0, 175002 (2017).
5 A. Ali, P. Laurian-Ioan, Geometric classification of warped products isometrically immersed in Sasakian space forms. Math. Nachr. 292, (2018), 234-251.   DOI
6 M. Atceken, Warped product semi-slant submanifolds in locally Riemannian product manifolds, Bull. Austral. Math. Soc., 77 (2008), 177-186.   DOI
7 M. Atceken, Contact CR-warped product submanifolds of Kenmotsu space forms, Bull. Iran. Math. Soc., 39(2013), 415-429.
8 F. R. Al-Solamy and M. A. Khan, Warped product submanifold of Riemannian product manifolds, Abstr. Appl. Anal. (2012), Article ID 724898.
9 F.R. Al-Solamy and S. Uddin, An inequality for warped product submanifolds of a locally product Riemannian manifold, Hacet. J. Math. Stat. Volume 48 (2) (2019), 351-358.
10 A. Bejancu, Semi-invariant submanifolds of locally product Riemannian manifolds, An. Univ. Timisoara, 22, (1984).
11 R. L. Bishop and B. O'Neil, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-9.   DOI
12 B.Y. Chen, Geometry of warped product CR-submanifold in Kaehler manifolds II, Monatsh. Math. 134 (2001), 103-119.   DOI
13 B.Y. Chen, Slant immersions, Bull. Austral. Math. Soc. 41 (1990), 135-147.   DOI
14 S. Hiepko, Eine inner kennzeichungder verzerrten produckt, Math. Ann. 244 (1979), 209-215.   DOI
15 H. Li and X. Li, Semi-slant submanifolds of locally product manifold, Georgian Math. J. 12 (2005), no-2., 273-282.   DOI
16 N. Papaghiuc, Semi-slant submanifold of Kaehler manifold, An. St. Univ. Al. I. Cuza. Iasi, 40 (1994), 55-61.
17 R. Ali and W.A. Othman. Geometric inequality of warped product semi-slant submanifolds of locally product Riemannian manifolds. Cogent Mathematics & Statistics. (2019): 1602017.
18 B. Sahin, Warped product semi-invariant submanifolds of a locally product Riemannian manifold, Bull. Math. Soc. Sci. Math. Roumanie, Tome 49 (97) No. 4, (2006), 383-394.
19 B. Sahin, Non-existence of warped product submanifolds of Kaehler manifolds, Geom. Dedicata, 117 (2006), 195-202.   DOI
20 A.N. Siddiqui, M.H. Shahid and J.W. Lee, Geometric inequalities for warped product bi-slant submanifolds with a warping function, J. Inequalities and Applications (2018) 2018:265
21 S. Uddin and F. R. Al-Solamy, Warped product pseudo-slant submanifolds of cosymplectic manifolds, Ann. St. Univ. Iasi, Tome 63 (2016): f2.
22 S. Uddin, A. Ali, N.M. Al-Asmari and W.A. Othman, Warped product pseudoslant submanifolds in a locally product Riemannian manifold, Differential Geometry - Dynamical Systems, Vol.18, 2016, pp. 147-158.